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Stability and instability of standing waves for 1-dimensional nonlinear Schrödinger equation with multiple-power nonlinearity. (English) Zbl 1180.35483

From the author’s abstract: We consider the stability and instability of standing waves for the following nonlinear Schrödinger equation: \[ iu_t+u_{xx}+f(u)=0,\quad t\geq 0,\;x\in \mathbb{R}, \] where \(f(u)=\sum^m_{j=1}a_j| u|^{p_j-1}u\) with \(a_j\in\mathbb{R}\) and \(1<p_1<\cdots<p_m<\infty\).

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B35 Stability in context of PDEs
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